In a “60 Minutes” interview raising eyebrows in status-obsessed Washington, outgoing Secretary of State Hillary Rodham Clinton said she and President Obama buried the hatchet after their 2008 campaign “because we both love our country.” Obama called Clinton one of the greatest diplomats in U.S. history.

And so ends a marriage of convenience that served both spouses well. Their relationship could be tested again if both Clinton and Vice President Joe Biden seek the presidency in 2016, forcing Obama to choose between two ambitious allies.

For now, it’s all roses. “I just wanted to have a chance to publicly say thank you because I think Hillary will go down as one of the finest secretary of states we’ve had,” Obama said in an excerpt of the interview posted on the CBS site Sunday. “I’m going to miss her. Wish she was sticking around.”

Clinton said “a few years ago it would have been seen as improbable” to stage an Obama-Clinton interview. But time heals: “Why did he ask me (to serve in the Cabinet) and why did I say yes?” she said, “Because we both love our country.”

There is another explanation for the teaming of rivals: Their union made good politics.

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For Obama, the relatively young and untested leader needed to unite his party in 2009, and he benefited from Clinton’s gravitas. The Cabinet post kept Clinton from wandering the political wilderness, and it burnished her already substantial presidential resume.

There also is a certain personal chemistry that was easily overlooked four years ago. Both the president and Clinton are extremely self-confident individuals (their critics call them arrogant) who despise Washington’s political culture. These are no-drama types who believe posturing and preening are beneath them as individuals and unworthy of the nation’s big challenges.

And yet: Obama and Clinton sat elbow-to-elbow during the "60 Minutes" interview, leaning into each other like an old and happily married couple reflecting on their time together.

"I consider Hillary to be a strong friend," Obama said. Clinton called their relationship "very warm, close. I think there is a sense of understanding. Sometimes, it doesn't even take words."

It was interesting, but not surprising, to watch as Obama almost always answered first when questions were posed to both of them. Reporter Steve Kroft said the White House gave "60 Minutes" just 30 minutes for the conversation, much of which he devoted to the politics of the relationship. Obama and Clinton deflected questions about Libya, Syria and their world view.

Their 2008 campaign was ugly. Clinton accused Obama of distorting her record and at one point snapped, “Shame on you, Barack Obama.” Her husband, former President Bill Clinton, questioned Obama’s fitness for the presidency in a series of condescending comments that briefly hurt his standing in the black community.

Obama famously issued a back-handed compliment aimed at Hillary Clinton’s personal appeal, or lack of it. “You’re likable enough, Hillary,” he said during a primary debate.

From all accounts, donors and staff members carried grudges far longer and deeper than did Obama and Clinton. For the first time, the pair confirmed to Kroft the greatest sources of friction: Michelle Obama and Bill Clinton. "I think spouses take it much harder," Obama said.

Their relationship started warming at the 2008 party convention, when both Clintons embraced Obama in their addresses. Obama said he recruited Clinton into his administration because he valued her stamina, discipline and thoughtfulness. Clinton said she was surprised by the offer and reluctant to accept but finally decided that "if the roles had been reversed and I had ended up winning I would have desperately wanted him to be in my Cabinet."

It would be easy to dismiss her claim as spin, particularly in such a managed setting. But Clinton is a pragmatic politician; those close to her and who have observed her career have long said she would have found a place in her Cabinet for Obama because, if for no other reason, she would have needed a united party.

As for 2016, Obama has told associates he wants to remain neutral, but that will be difficult. Biden and Clinton both have a rightful claim to the nomination and to Obama’s endorsement. And the media will be clamoring for a Clinton-Biden matchup because, as I have written, it would be a hoot.

Indeed, Kroft asked about the "expiration date" on what he suggested was a 2016 endorsement.

"Steve," Obama bristled, "I've got to tell you: You guys in the press are incorrigible." He glanced at his watch and added, "I was literally inaugurated four days ago and you're talking about an election four years from now."

UPDATE: The initial version of this story was based on an excerpt of the interview. It was updated after the show's broadcast.